Let

be the function given by

for

.

a) Calculate the fourier coefficients of

and show that...

for

for

.

done...

b) What is the Fourier series of

in terms of sines and cosines?

My answer,

.

For even n's the summands of this series are zero, so you can take only odd n's in the sum and since you have a square in the denominator this is the same as twice the sum over the odd natural numbers (taking ): . Now equal the above to zero and you'll get what you want... Tonio
c) Taking

, prove that

and

Now this, I suspect, should have just been a simple application of Parsevals theorem but I'm going wrong somewhere.

**Parsevals Theorem.**
But with

the left hand side is 0.

Thus we get,

=

So clearly I'm doing something wrong... Most likely in that last 2 steps...